Cambridge IGCSE Mathematics - International 0607 — 2013 May/June Paper 2 · Variant 1

This document consists of 8 printed pages. IB13 06_0607_21/3RP © UCLES 2013 [Turn over *1024033730* UNIVERSITY OF CAMBRIDGE INTERNATIONAL EXAMINATIONS International General Certificate of Secondary Education CAMBRIDGE INTERNATIONAL MATHEMATICS 0607/21 Paper 2 (Extended) May/June 2013 45 minutes Candidates answer on the Question Paper. Additional Materials: Geometrical Instruments READ THESE INSTRUCTIONS FIRST Write your Centre number, candidate number and name on all the work you hand in. Write in dark blue or black pen. Do not use staples, paper clips, highlighters, glue or correction fluid. You may use a pencil for any diagrams or graphs. DO NOT WRITE IN ANY BARCODES. Answer all the questions. CALCULATORS MUST NOT BE USED IN THIS PAPER. All answers should be given in their simplest form. You must show all the relevant working to gain full marks and you will be given marks for correct methods even if your answer is incorrect. The number of marks is given in brackets [ ] at the end of each question or part question. The total number of marks for this paper is 40. www.XtremePapers.com

2 © UCLES 2013 0607/21/M/J/13 Formula List For the equation ax2 + bx + c = 0 x = 2 _ ± 4 2 _ b b ac a Curved surface area, A, of cylinder of radius r, height h. A = 2πrh Curved surface area, A, of cone of radius r, sloping edge l. A = πrl Curved surface area, A, of sphere of radius r. A = 4πr2 Volume, V, of pyramid, base area A, height h. V= 1 3 Ah Volume, V, of cylinder of radius r, height h. V = πr2h Volume, V, of cone of radius r, height h. V = 1 3 πr2h Volume, V, of sphere of radius r. V = 4 3 πr3 = = sin sin sin a b c A B C a2 = b2 + c2 – 2bc cos A Area = 1 2 bc sin A A a B C b c

3 © UCLES 2013 0607/21/M/J/13 [Turn over For Examiner's Use Answer all the questions. 1 The population of India in 2011 was 1.21 × 109 . The population of Pakistan in 2011 was 1.77 × 108 . Calculate the total population of India and Pakistan in 2011. Give your answer in standard form. Answer [2] 2 P is the point (–2, 5) and Q is the point (4, 1). (a) Find the co-ordinates of the midpoint of PQ. Answer(a) ( , ) [1] (b) Find the gradient of PQ. Answer(b) [2] (c) (i) Find the equation of the line perpendicular to PQ which passes through the point (0, 4). Answer(c)(i) [2] (ii) Find the x co-ordinate of the point where this line cuts the x-axis. Answer(c)(ii) x = [1]

4 © UCLES 2013 0607/21/M/J/13 For Examiner's Use 3 Solve these simultaneous equations. y = 2x – 8 3x + 2y = 5 Answer x = Answer y = [3] 4 One morning, Ashad carries out a survey on the colours of 200 cars in his town. These are his results. Colour Silver Black Red Blue Other Frequency 78 40 36 30 16 (a) Complete this table of relative frequencies. Colour Silver Black Red Blue Other Relative Frequency 0.2 [2] (b) There is a total of 18 000 cars in the town. Work out an estimate of the number of black cars in the town. Answer(b) [2]

5 © UCLES 2013 0607/21/M/J/13 [Turn over For Examiner's Use 5 y° x° 130° A B O D C E NOT TO SCALE A, B, C and D are points on the circle centre O. DCE is a straight line. Angle AOD = 130°. Find the value of (a) x, Answer(a) x = [2] (b) y. Answer(b) y = [2]

6 © UCLES 2013 0607/21/M/J/13 For Examiner's Use 6 U P Q R On the Venn diagram write the elements a, b and c in the correct subsets using the following information. a ∈ (P ∪ Q ∪ R)' b ∈ P ' ∩ (Q ∩ R) c ∈ (Q ∪ R)' ∩ P [3] 7 (a) Write down the value of (i) log 1000, Answer(a)(i) [1] (ii) log 0.01 . Answer(a)(ii) [1] (b) Find p when 2log 5 – log 2 = log p . Answer(b) p = [2]

7 © UCLES 2013 0607/21/M/J/13 [Turn over For Examiner's Use 8 5 cm r cm 160° NOT TO SCALE The diagrams show a circle with radius 5 cm and the sector of another circle with angle 160° and radius r cm. The circle and the sector have the same area. Calculate the value of r. Answer r = [4] 9 Simplify. (a) 50 + 8 Answer(a) [2] (b) ( 3 5 + ) 2 Answer(b) [2] Questions 10 and 11 are printed on the next page.

8 Permission to reproduce items where third-party owned material protected by copyright is included has been sought and cleared where possible. Every reasonable effort has been made by the publisher (UCLES) to trace copyright holders, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity. University of Cambridge International Examinations is part of the Cambridge Assessment Group. Cambridge Assessment is the brand name of University of Cambridge Local Examinations Syndicate (UCLES), which is itself a department of the University of Cambridge. © UCLES 2013 0607/21/M/J/13 For Examiner's Use 10 Rearrange this equation to make x the subject. ax – 3y = b(x + 2y) Answer x = [3] 11 a b p q r Write the vectors p, q and r in terms of a and b. Answer p = q = r = [3]

CAMBRIDGE INTERNATIONAL EXAMINATIONS International General Certificate of Secondary Education MARK SCHEME for the May/June 2013 series 0607 CAMBRIDGE INTERNATIONAL MATHEMATICS 0607/21 Paper 2 (Extended), maximum raw mark 40 This mark scheme is published as an aid to teachers and candidates, to indicate the requirements of the examination. It shows the basis on which Examiners were instructed to award marks. It does not indicate the details of the discussions that took place at an Examiners’ meeting before marking began, which would have considered the acceptability of alternative answers. Mark schemes should be read in conjunction with the question paper and the Principal Examiner Report for Teachers. Cambridge will not enter into discussions about these mark schemes. Cambridge is publishing the mark schemes for the May/June 2013 series for most IGCSE, GCE Advanced Level and Advanced Subsidiary Level components and some Ordinary Level components. www.XtremePapers.com

Page 2 Mark Scheme Syllabus Paper IGCSE – May/June 2013 0607 21 © Cambridge International Examinations 2013 1 1.387 × 109 2 B1 for figs 1387 or 12.1 × 108 or 0.177 × 109 2 (a) (1, 3) 1 (b) – 3 2 o.e. –0.667 or better 2 M1 for clear attempt at y increase / x increase (c) (i) y = 2 3 x + 4 2FT M2FT for y = (–1/their (b))x + 4 M1 for m = –1/their (b) (ii) – 3 8 o.e. –2.67 or better 1FT FT from their (c)(i) but not from y = kx 3 x = 3 y = –2 3 M1 for correct equation in 1 variable A1 for each answer 4 (a) 0.39, (0.2), 0.18, 0.15, 0.08 2 B1 for any 3 seen (b) 3600 2 M1 for 0.2 × 18 000 o.e. 5 (a) 115° 2 B1 for reflex angle AOD = 230° or cyclic quad drawn with angle 65° (b) 65° 2FT FT 180 – their (a) B1 for angle ACD = their (a) (=x) 6 3 1 for each correctly placed 7 (a) (i) 3 1 (ii) –2 1 (b) 12.5 2 B1 for log5² or log2p or logk/2 seen 8 7.5 4 M1 for 360 160 × π × r² M1 for their sector = π × 25 M1 for elimination of π 9 (a) 7 2 2 B1 for 5 2 or 2 2 seen (b) 28 + 10 3 2 B1 for 25 + 5 3 + 5 3 + 3 × 3 U P Q R c b a

Page 3 Mark Scheme Syllabus Paper IGCSE – May/June 2013 0607 21 © Cambridge International Examinations 2013 10 2by + 3y o.e. a – b 3 B1 for bx + 2by M1 for correctly isolating x terms M1 for correctly factorising and dividing by bracket 11 a + b – 2 1 a – b 2b – a 1 1 1 All answers must be in the form pa + qb